Using Multivariate Statistics

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Using Multivariate Statistics provides advanced students with a timely and comprehensive introduction to todayrs"s most commonly encountered statistical and multivariate techniques, while assuming only a limited knowledge of higher level mathematics. This long-awaited revision reflects extensive updates throughout, especially in the areas of Data Screening (Chapter 4), Multiple Regression (Chapter 5), and Logistic Regression (Chapter 12). A brand new chapter (Chapter 15) on Multilevel Linear Modeling explains techniques for dealing with hierarchical data sets. Also included are syntax and output for accomplishing many analyses through the most recent releases of SAS and SPSS. As in past EDITIONs, each technique chapter: bull; discusses tests for assumptions of analysis (and procedures for dealing with their violation) bull; presents a small example, hand-worked for the most basic analysis bull; describes varieties of analysis bull; discusses important issues (such as effect size) bull; provides an example with a real data set from tests of assumptions to write-up of a results section bull; compares features of relevant programs

Preface

xxvii

Introduction

1

(16)

Multivariate Statistics: Why?

1

(4)

The Domain of Multivariate Statistics: Numbers of IVs and DVs

1

(1)

Experimental and Nonexperimental Research

2

(2)

Computers and Multivariate Statistics

4

(1)

Garbage In, Roses Out?

5

(1)

Some Useful Definitions

5

(5)

Continuous, Discrete, and Dichotomous Data

5

(2)

Samples and Populations

7

(1)

Descriptive and Inferential Statistics

7

(1)

Orthogonality: Standard and Sequential Analyses

8

(2)

Linear Combinations of Variables

10

(1)

Number and Nature of Variables to Include

11

(1)

Statistical Power

11

(1)

Data Appropriate for Multivariate Statistics

12

(4)

The Data Matrix

12

(1)

The Correlation Matrix

13

(1)

The Variance-Covariance Matrix

14

(1)

The Sum-of-Squares and Cross-Products Matrix

14

(2)

Residuals

16

(1)

Organization of the Book

16

(1)

A Guide to Statistical Techniques: Using the Book

17

(16)

Research Questions and Associated Techniques

17

(10)

Degree of Relationship among Variables

17

(1)

Bivariate r

17

(1)

Multiple R

18

(1)

Sequential R

18

(1)

Canonical R

18

(1)

Multiway Frequency Analysis

19

(1)

Multilevel Modeling

19

(1)

Significance of Group Differences

19

(1)

One-Way ANOVA and t Test

19

(1)

One-Way ANCOVA

20

(1)

Factorial ANOVA

20

(1)

Factorial ANCOVA

20

(1)

Hotelling's T2

21

(1)

One-Way MANOVA

21

(1)

One-Way MANCOVA

21

(1)

Factorial MANOVA

22

(1)

Factorial MANCOVA

22

(1)

Profile Analysis of Repeated Measures

23

(1)

Prediction of Group Membership

23

(1)

One-Way Discriminant

23

(1)

Sequential One-Way Discriminant

24

(1)

Multiway Frequency Analysis (Logit)

24

(1)

Logistic Regression

24

(1)

Sequential Logistic Regression

25

(1)

Factorial Discriminant Analysis

25

(1)

Sequential Factorial Discriminant Analysis

25

(1)

Structure

25

(1)

Principal Components

25

(1)

Factor Analysis

26

(1)

Structural Equation Modeling

26

(1)

Time Course of Events

26

(1)

Survival/Failure Analysis

26

(1)

Time-Series Analysis

27

(1)

Some Further Comparisons

27

(1)

A Decision Tree

28

(3)

Technique Chapters

31

(1)

Preliminary Check of the Data

32

(1)

Review of Univariate and Bivariate Statistics

33

(27)

Hypothesis Testing

33

(4)

One-Sample z Test as Prototype

33

(3)

Power

36

(1)

Extensions of the Model

37

(1)

Controversy Surrounding Significance Testing

37

(1)

Analysis of Variance

37

(16)

One-Way Between-Subjects ANOVA

39

(3)

Factorial Between-Subjects ANOVA

42

(1)

Within-Subjects ANOVA

43

(3)

Mixed Between-Within-Subjects ANOVA

46

(1)

Design Complexity

47

(1)

Nesting

47

(1)

Latin-Square Designs

47

(1)

Unequal n and Nonorthogonality

48

(1)

Fixed and Random Effects

49

(1)

Specific Comparisons

49

(1)

Weighting Coefficients for Comparisons

50

(1)

Orthogonality of Weighting Coefficients

50

(1)

Obtained F for Comparisons

51

(1)

Critical F for Planned Comparisons

52

(1)

Critical F for Post Hoc Comparisons

53

(1)

Parameter Estimation

53

(1)

Effect Size

54

(2)

Bivariate Statistics: Correlation and Regression

56

(2)

Correlation

56

(1)

Regression

57

(1)

Chi-Square Analysis

58

(2)

Cleaning Up Your Act: Screening Data Prior to Analysis

60

(57)

Important Issues in Data Screening

61

(31)

Accuracy of Data File

61

(1)

Honest Correlations

61

(1)

Inflated Correlation

61

(1)

Deflated Correlation

61

(1)

Missing Data

62

(1)

Deleting Cases or Variables

63

(3)

Estimating Missing Data

66

(4)

Using a Missing Data Correlation Matrix

70

(1)

Treating Missing Data as Data

71

(1)

Repeating Analyses with and without Missing Data

71

(1)

Choosing among Methods for Dealing with Missing Data

71

(1)

Outliers

72

(1)

Detecting Univariate and Multivariate Outliers

73

(3)

Describing Outliers

76

(1)

Reducing the Influence of Outliers

77

(1)

Outliers in a Solution

77

(1)

Normality, Linearity, and Homoscedasticity

78

(1)

Normality

79

(4)

Linearity

83

(2)

Homoscedasticity, Homogeneity of Variance, and Homogeneity of Variance-Covariance Matrices